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R

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I

R

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Since the current is the same throughout a series circuit, this is a simple method for finding the current in both the resistor and capacitor. Enter the computed current in Table 2-1-2.

Compute the capacitive reactance, XC, by applying Ohm’s Law to the Capacitor. The reactance is found by dividing the voltage across the capacitor (step 3) by the current in the circuit (step 4). Enter the Capacitive reactance in the Table 2-1-2.

Frequency	VR	VC	I	XC	Z
500 Hz.
1000 Hz.
1500 Hz.
2000 Hz.
4000 Hz.
8000 Hz.

Table 2-1-2

Compute the total impedance in the circuit by applying Ohm’s law to the entire circuit. Use the generator voltage set in step 2 and current determined on step 4. Enter the computed impedance in Table 2-1-2.

Change the frequency of the generator to 1000 Hz. Check the Generator Voltage and reset it to 3.0 VPP if necessary. Repeat steps 3 through 6, entering the data in Table 2-1-2 Continue in this manner for each frequency listed in Table 2-1-2.

From the data in the Table 2-1-2 and the measured value of R1, draw the impedance phasors for the circuit at a frequency of 1000 Hz. on Plot 3-1-1(a) and the voltage phasors on Plot 3-1-1(b).

Plot 3-1-1

Repeat step 8 for a frequency of 4000Hz. Draw the impedance phasor on

Plot 3-1-2(a) and the voltage phasor on Plot 3-1-2(b).

Plot 3-1-2

The Phasor drawings reveal how the impedance and voltage phasors change with frequency. Investigate the frequency effect further by graphing both the voltage across the capacitor and the voltage across the resistor as a function of frequency. Label each curve. Use Plot 3-1-3.

Plot 3-1-3

Experiment #2: Parallel RC Circuits:

Objectives:

After Performing this experiment, you will be able to:

Measure the current phasors for a parallel RC circuit.

Explain how the current phasors and phase angle are affected by a change in frequency for parallel RC circuits.

Materials Required:

Resistors: 100 kΩ - 1 Piece, 1.0 kΩ- 2 Pieces.

Capacitors: 1000pF- 1 Piece.

Summary of Theory:

In a series circuit, the same current is in all the components. For this reason, current is generally used as the reference. By contrast, in parallel, the same voltage is present across all the components. Voltage is therefore the reference for parallel circuits. Current in each branch is compared to the circuit voltage. In parallel circuits, Kirchoff’s current law applies to any junction but care must be taken to add the currents as phasors. The current entering a junction is always equal to the current leaving the junction.

Figure 2-2-1 illustrates an example of a parallel RC circuit. If the impedance of each branch is known, the current in that branch can be determined directly from Ohm’s law. The current phasor diagram can then be constructed. The total current can be found as the phasor sum of the currents in each branch. The current in the capacitor is shown at + 90o from the voltage reference because the current leads the voltage in a capacitor. The current in the resistor is along the x-axis because current and voltage are in phase in the resistor. The Pythagorean Theorem can be applied to the current phasors, resulting in the following equation.

Figure: 2-2-1 (a)

Figure: 2-2-1 (b)

Note: In this experiment, two extra 1.0 kΩ resistors are added to “ sense ” current and provide a small voltage drop that can be measured. These resistors are much smaller than parallel branch impedance, so their resistance can be ignored in computation of circuit impedance.

Procedure:

Measure a resistor with a color-code value of 100 kΩ and each of two current-sense resistors (Rs1 and Rs2) with color-code values of 1.0 kΩ. Measure the capacitance of a 1000 pF capacitor. Use the listed value if a measurement cannot be made. Record the measured values in Table 2-2-1.

Table 2-2-1

Figure 2-2-2

Construct the circuit shown in Fig 2-2-2. Set the generator to a voltage of

3.0 Vrms at 1.0 kHz. Check the voltage and frequency with your oscilloscope.

Using a voltmeter, measure the voltage drop across each resistor. The voltage drops are small, so measure as accurately as possible. You should keep at least three significant figures in your measurement. Record the voltage drops in

Table 2-2-1.

Compute the current in each resistor using Ohm’s Law. Record the computed current in Table 2-2-1.

Draw the current phasors IR1, IC1 and the total current IT on the Plot 3-2-1. The total current is through the sense resistor RS1. The current IC1 is through the sense resistor RS2. Ignore the small effect of the sense resistors on the Phasor diagram. Note carefully the direction of the phasor. Label each of the current phasors.

Plot 2-2-1

Compute XC1 for the 1.0 kHz. Frequency. Then using this value and the measured resistance of R1 find the total impedance, ZT of the circuit using the product over sum rule as given below. The sense resistors can be ignored for this calculation

Using ZT from step 6 and the applied voltage, Vs, Compute the total current, IT. The total current should basically agree with the value determined in step 4.

IT = .

8. Change the frequency of the generator to 2.0 kHz. Check the generator voltage is still 3.0 V. Repeat steps 1-5 for the 2.0 kHz. Frequency. Enter the data in Table 2-2-2 and draw the current phasors on the Plot 3-2-2.

Table 2-2-2

Plot 3-2-2